I read some similar questions like Simply put, what does “perfect secrecy” mean? (This one defines perfect secrecy as ciphertext conveys no information about the content of the plaintext.
Now, problem 2.3 on this assignment asks:
show that perfect secrecy of $(GEN, ENC, DEC)$ implies $$\Pr [ENC_k(m) = c] = \Pr [ENC_k(m') = c]$$
Isn't the above equation saying that ciphertext $c$ gives no information whether it's $m$ or $m'$?
What is the exact definition of perfect secrecy then?
P.S. the assignment link above contains the solution. In the solution, I don't understand where the definition of perfect secrecy is used, nor what it is.